Multichannel detection for correlated non-Gaussian random processes based on innovations

The paper addresses the problem of multichannel signal detection in additive correlated non-Gaussian noise using the innovations approach. Although this problem has been addressed extensively for the case of additive Gaussian noise, the corresponding problem for the non-Gaussian case has received limited attention. This is due to the fact that there is no unique specification for the joint probability density function (PDF) of N correlated non-Gaussian random variables. The authors overcome this problem by using the theory of spherically invariant random processes (SIRPs) and derive the innovations-based detector. It is found that the optimal estimators for obtaining the innovations, processes are linear and that the resulting detector is canonical for the class of PDFs arising from SIRPs. The authors also present a performance analysis of the innovations-based detector for the case of a K-distributed SIRP